It can be equivalently written as
One should not confuse the polydisc with the open ball in Cn, which is defined as
When , open balls and open polydiscs are not biholomorphically equivalent, that is, there is no biholomorphic mapping between the two. This was proven by Poincaré in 1907 by showing that their automorphism groups have different dimensions as Lie groups.
When the term bidisc is sometimes used.
- Poincare, H,Les fonctions analytiques de deux variables et la r?epresentation conforme, Rend. Circ. Mat. Palermo23 (1907), 185-220
- Steven G Krantz (Jan 1, 2002). Function Theory of Several Complex Variables. American Mathematical Society. ISBN 0-8218-2724-3.
- John P D'Angelo, D'Angelo P D'Angelo (Jan 6, 1993). Several Complex Variables and the Geometry of Real Hypersurfaces. CRC Press. ISBN 0-8493-8272-6.